You should definitely check out the H and HH models in both the old style and new Special. I have not played the new Special. It's 18v preamp may make a huge difference on the HH models. Or it may not.
To throw out some more info, the 30th Anniversary Stingray 5 H sounds a little different from the standard H models and NeckThrough models have a little different tone as well. There is also the Classic model, which only comes in H and has a 2-band EQ with no switch.
Good point that the OP should consider. The different variations do sound slightly different. I have a first-year '88 SR5, a 30th anniversary SR5, and a new SR5 Special (I also had the SR5HH from 2014 that I sold a few months back) and they all sound slightly different from each other when comparing just the bridge pickup. The '88 is much more harsh and aggressive sounding; the 30th anniversary is tamer but the next most aggressive (it has a revised preamp and ceramic pickup magnets rather than alnico), the SR5HH had the modern StingRay tone that cut, but was more warm (alnico and parallel-only wiring); the 5H Special is the least aggressive of the bunch (though it certainly cuts like a StingRay and be EQ'd to get pretty gnarly), but has the most powerful preamp of the bunch. I was amazed at how the 5H Special could get close to many of the tones of the 5HH with just preamp tweaks. While they all sound slightly different, they all have the unmistakeable StingRay tone, just slightly different flavors.
From what I remember, StingRay 5 basses evolved something like this over the years:
'88 - '91/'92 (I've seen both years referenced): Alnico pickup magnets, series/single coil (no dummy coil)/parallel wiring
'92 - '08: Ceramic pickup magnets (the HH was introduced in '06, so you have some out there with ceramic pickup magnets and then others starting in '08 with alnico magnets)
'08 - '17: back to alnico pickup magnets (except the 2017 30th anniversary SR5 which is a different preamp and ceramic pickup magnets)
'18: Special introduced with 18v preamp and neodymium pickup magnets
There were other changes in there, too, like the single coil/filter setting on the 5H, but I don't remember when those occurred.